> Your right, the engineer who analyzed the plant response knows
> where the poles and zeros are, and his closed form algorithm
> provides the gain and phase compensation.
>
> >And, most importantly, physical processes don't have poles & zeros,
> >anyway. The poles & zeros are a feature of your mathematical model of
> >the process.
>
> I don't know where you studied control theory, but If you are using
> a linear time-invariant system to control a physical process, It
> had better have a response in the frequency domain.
>
> >There is no reason that I know of to believe that there
> >are no other valid models of physical processes, or to
> >believe that other models might not be as good.
>
> I didn't say there were no other valid models.  I said if you have
> a model which in closed form, you know what compensation will
> provide stability for all time.

I think one of the issues with fuzzy systems is that real-life systems
seldom exhibit ideal linear behavior; PID systems can be unstable or
conditionally-stable on such systems and changing system behavior can
change controller response.  While fuzzy systems will seldom have closed-
loop behavior as good as a perfectly-tuned PID system, they can often be
made less sensitive to system characteristics.

As a (very) rough analogy, a camera lens which is designed to focus perfectly
at a certain distance will be very sensitive to changes in that distance;
objects at other distances will be out of focus.  By contrast, a lens which
is focuses less well at is focusing distance may blur less at other distances.
The extreme example of this is a pinhole camera which blurs objects at all
distances roughly uniformly.